You really should learn to post in LaTeX. It hard to know exactly what you are asking.
Your table seems to be:
$\displaystyle \begin{array}{*{20}{c}} {{n^k}}&{n(n - 1) \cdots (n - k + 1)} \\ {\binom{n-1+k}{k}}&{\binom{n}{k}} \end{array}$
Is that correct?
If so the "upper right hand formula" is the permutation of $\displaystyle N$ choosing $\displaystyle k$.
i.e. $\displaystyle _N\mathcal{P}_k=\frac{N!}{(N-k)!}$.